Optimal Output Regulation for Switched Boolean Control Networks
摘要
This paper investigates the optimal output regulation of switched Boolean control networks by using a dynamic programming method. The reference signal studied in this paper is generated by the output trajectory of a switched Boolean network. First, a per-step cost vector is proposed based on the largest control invariant set of the augmented auxiliary system. Then, a novel criterion is derived for determining the solvability of the output regulation. The proposed criterion transforms the solvability of output regulation of switched Boolean control networks into an optimization problem, providing a new perspective for addressing output regulation through optimal control. Based on this, an optimal state feedback control is proposed to enable the output trajectory of the original network to completely track the reference signal. An algorithm is presented to calculate the optimal feedback gain matrix and the optimal value for each state. Compared with existing results, the optimal state feedback control presented in this paper offers a generalized optimization principle and effectively reduces the computational complexity associated with designing state feedback control. Finally, an illustrative example is provided to validate the effectiveness of the results obtained.